TITLE:
Second-Order MaxEnt Predictive Modelling Methodology. III: Illustrative Application to a Reactor Physics Benchmark
AUTHORS:
Ruixian Fang, Dan Gabriel Cacuci
KEYWORDS:
Second-Order Predictive Modeling, OECD/NEA Reactor Physics Benchmark, Data Assimilation, Best-Estimate Results, Uncertainty Quantification, Reduced Predicted Uncertainties
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.13 No.2,
June
21,
2023
ABSTRACT: This work illustrates the innovative
results obtained by applying the recently developed the 2nd-order
predictive modeling methodology called “2nd- BERRU-PM”, where the
acronym BERRU denotes “best-estimate results with reduced uncertainties” and
“PM” denotes “predictive modeling.” The physical system selected for this
illustrative application is a polyethylene-reflected plutonium (acronym: PERP)
OECD/NEA reactor physics benchmark. This benchmark is modeled using the neutron
transport Boltzmann equation (involving 21,976 uncertain parameters), the
solution of which is representative of “large-scale computations.” The results
obtained in this work confirm the fact that the 2nd-BERRU-PM
methodology predicts best-estimate results that fall in between the
corresponding computed and measured values, while reducing the predicted
standard deviations of the predicted results to values smaller than either the
experimentally measured or the computed values of the respective standard
deviations. The obtained results also indicate that 2nd-order
response sensitivities must always be included to quantify the need for
including (or not) the 3rd- and/or 4th-order
sensitivities. When the parameters are known with high precision, the
contributions of the higher-order sensitivities diminish with increasing order,
so that the inclusion of the 1st- and 2nd-order
sensitivities may suffice for obtaining accurate predicted best- estimate response
values and best-estimate standard deviations. On the other hand, when the
parameters’ standard deviations are sufficiently large to approach (or be
outside of) the radius of convergence of the multivariate Taylor-series which
represents the response in the phase-space of model parameters, the
contributions stemming from the 3rd- and even 4th-order
sensitivities are necessary to ensure consistency between the computed and
measured response. In such cases, the use of only the 1st-order
sensitivities erroneously indicates that the computed results are inconsistent
with the respective measured response. Ongoing research
aims at extending the 2nd-BERRU-PM methodology to fourth-order, thus
enabling the computation of third-order response correlations (skewness) and
fourth-order response correlations (kurtosis).